Cumulant based identification approaches for nonminimum phase FIR systems

Cataloged from PDF version of article.In this paper, recursive and least squares methods for identification of nonminimum phase linear time-invariant (NMP-LTI) FIR systems are developed. The methods utilize the second- and third-order cumulants of the output of the FIR system whose input is an independent, identically distributed (i.i.d.) non-Gaussian process. Since knowledge of the system order is of utmost importance to many system identification algorithms, new procedures for determining the order of an FIR system using only the output cumulants are also presented. To illustrate the effectiveness of our methods, various simulation examples are presented

Fir system identification using a linear combination of cumulants

A general linear approach to identifying the parameters of a moving average (MA) model from the statistics of the output is developed. It is shown that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. This result is then used to obtain a new well-conditioned linear method to estimate the MA parameters of a nonGaussian process. The proposed approach does not require a previous estimation of the filter order. Simulation results show improvement in performance with respect to existing methods.Peer ReviewedPostprint (published version

A Phase Reconstruction Algorithm From Bispectrum

A new computationally efficient procedure for the reconstruction of the impulse response of a (minimum or nonminimum phase) linear time-invariant (LTI) system from its bispectrum is presented. This method is based on computing the cepstrum of the impulse response sequence from the ω1 = ω2 slice of the bispectrum. The algorithm can be implemented by using only the one-dimensional fast Fourier transform algorithm. © 1990 IEE

Cumulant-based identification of non gaussian moving average signals

In this paper, an overview on higher-order statistics based identification methods is presented, and tree batch blind estimation methods are proposed . One of them use both autocorrelation and cumulant sequences, the others are cumulant-based only . The cumulant-based ones are respectively a generalization of Zhang et al.'s method and a reformulation of Giannakis-Mendel's method without autocorrelation . By simulations, we evaluate their performances and compare them together and with the existing approaches. The results show that the generalization of Zhang et al.'s method give good estimates, specially in noise environment (white or colored noises) .Dans ce papier, nous donnons un aperçu des méthodes classiques d'identification des signaux linéaires non gaussiens de type à moyenne ajustée basées sur les statistiques d'ordre supérieur (SOS). Puis, nous proposons trois méthodes d'estimation globale : la première combine l'autocorrélation et les cumulants et les deux autres exploitent les cumulants seuls. L'une d'entre elles généralise la méthode de Zhang et al., La deuxième est une modification de l'approche reformulée de Giannakis et Mendel. Elle est obtenue en remplaçant les moments d'ordre deux, sensibles aux bruits gaussiens, par des cumulants, grâce à une relation qu'on développera. Finalement nous testons par simulations les performances des trois méthodes proposées et nous les comparons à d'autres approches existantes. Les résultats montrent que la méthode proposée généralisant celle de Zhang et al., fournit de bons résultats et qu'elle est plus résistante aux effets des bruits blancs ou colorés

Spectral estimation for mixed causal-noncausal autoregressive models

This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the innovations. Instead, we use the information of higher-order cumulants, combining the spectrum and the bispectrum in a minimum distance estimation. We show how to circumvent the nonlinearity of the parameters and the multimodality in the noncausal and mixed models by selecting the appropriate initial values in the estimation. In addition, we propose a method of identification using a simple comparison criterion based on the global minimum of the estimation function. By means of a Monte Carlo study, we find unbiased estimated parameters and a correct identification as the data depart from normality. We propose an empirical application on eight monthly commodity prices, finding noncausal and mixed causal-noncausal dynamics

System identification using a linear combination of cumulant slices

In this paper we develop a new linear approach to identify the parameters of a moving average (MA) model from the statistics of the output. First, we show that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, this result is used to obtain a new well-conditioned linear method to estimate the MA parameters of a non-Gaussian process. The proposed method presents several important differences with existing linear approaches. The linear combination of slices used to compute the MA parameters can be constructed from dif- ferent sets of cumulants of different orders, providing a general framework where all the statistics can be combined. Further- more, it is not necessary to use second-order statistics (the autocorrelation slice), and therefore the proposed algorithm still provides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while most linear methods developed so far give totally erroneous estimates if the order is overestimated, the proposed approach does not require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to existing methods.Peer Reviewe